Find ten equation of the plane passing through the point `(0,7,-7)` and containing the line `(x+1)/(-3)=(y-3)/2=(z+2)/1` .

Options

A. `x+y+z=1`
B. `x+y+z=2`
C. `x+y+z=0`
D. None of these

Answer

C

Explanation

The equation of plane containing the line
`(x+1)/(-3)=(y-3)/(2)=(z+2)/(1)` is
`a(x+1)+b(y-3)+c(z+2)=0" ...(i)`
where `-3a+2b+c=0" "....(ii)`
This passses through `(0,7,7)`
`:. A+4b-5c=0 " "....(iii)`
From Eqa. (ii) and (iii).
`(a)/(-14)=(b)/(-14)=(c)/(-14)`
or `(a)/(1)=(b)/(1)=(c)/(1)`
Thus, the requried plane is `++y+z=0`